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Complex biological networks, encompassing metabolic pathways, gene regulatorysystems, and protein-protein interaction networks, often exhibit scale-freestructures characterized by heavy-tailed degree distributions. However,empirical studies reveal significant deviations from ideal power law behavior,underscoring the need for more flexible and accurate probabilistic models. Inthis work, we propose the Compounded Burr (CBurr) distribution, a novel fourparameter family derived by compounding the Burr distribution with a discretemixing process. This model is specifically designed to capture both the bodyand tail behavior of real-world network degree distributions with applicationsto biological networks. We rigorously derive its statistical properties,including moments, hazard and risk functions, and tail behavior, and develop anefficient maximum likelihood estimation framework. The CBurr model demonstratesbroad applicability to networks with complex connectivity patterns,particularly in biological, social, and technological domains. Extensiveexperiments on large-scale biological network datasets show that CBurrconsistently outperforms classical power-law, log-normal, and otherheavy-tailed models across the full degree spectrum. By providing astatistically grounded and interpretable framework, the CBurr model enhancesour ability to characterize the structural heterogeneity of biologicalnetworks.

A Compounded Burr Probability Distribution for Fitting Heavy-Tailed Data with Applications to Biological Networks